4The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is0.4, the analogous probability for the second signal is0.45, and the probability that he must stop at at least one of the two signals is0.75.

(a) What is the probability that he must stop at both signals?

(b) What is the probability that he must stop at the first signal but not at the second one?

(c) What is the probability that he must stop at exactly one signal?

13.According to a posting on a website subsequent to the death of a child who bit into a peanut, a certain study found that9% of children younger than 18 in the United States have at least one food allergy. Among those with food allergies, about37% had a history of severe reaction.

(a)

If a child younger than 18 is randomly selected, what is the probability that he or she has at least one food allergy and a history of severe reaction? (Enter your answer to four decimal places.)

(b)

It was also reported that40% of those with an allergy in fact are allergic to multiple foods. If a child younger than 18 is randomly selected, what is the probability that he or she is allergic to multiple foods? (Enter your answer to three decimal places.)